yes, this is absolutely according to AdWords policies. Your competitor can also use your client's brand name in his ads, unless your client does have trademark for it. But there are absolutely no limitations for brand name/trademarks in keywords.

Client's Brand Name being used in Competitor's Google Adwords campaign

Yes you can use a competitors brand terms as targeted KW's. No, you can't use a competitors brand name in your ads - Regardless of whether or not that brand is legally TM'd. Sometimes it may happen, TM or no, but as soon as someone files a complaint, those ads will get disapproved.